Question

You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20? Using the information in the problem above; How many years will it take if monthly compounding, assuming everything else is the same? (Round to tenth decimal)

Answer 1

a.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

9140.2=5000*(1.08)^n

(9140.2/5000)=(1.08)^n

Taking log on both sides;

log(9140.2/5000)=n*log 1.08

n=log(9140.2/5000)/log 1.08

which is equal to

=7.84 years

=7.8 years(Approx).

2.

We use the formula:
A=P(1+r/1200)^12n
where
A=future value
P=present value
r=rate of interest
n=time period.

9140.2=5000(1+0.08/12)^12n

(9140.2/5000)=(1+0.08/12)^12n

Taking log on both sides;

log(9140.2/5000)=12n*log (1+0.08/12)

12n=log(9140.2/5000)/log1.00667

n=1/12[log(9140.2/5000)/log1.00667]

=7.6 years(Approx).